I don't think there are very many (good) campgrounds in CC. Most folks stay in Rockport, Aransas Pass or Port Aransas. Visit RV Park Reviews, lots of choices around CC.

http://www.rvparkreviews.com/

The State park on Galveston Island is great with the beach in your face. Most of the RV Parks on the Island are a little shabby (IMHO). The nicest is Galveston Island RV Resort.

http://www.galveston.com/galvestonrvpark/

If you are coming into Galveston on I45 there is a great RV Park about 10 miles from Galveston.

http://www.oasis45.com/

Lots of great seafood in Port Aransas

I forgot to mention another pretty new park on Galveston island that I have heard is nice. Jamaica Beach RV park is on the southern end of the island, I think just past midway.